Using Gnuplot

8/12/2019 Using Gnuplot

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COMPUTERS, CHEMISTRY, AND MISC.

Gnuplotis a very powerful plotting program that can generate publication-quality

images and plots. It creates both 2-dimensional plots and 3-dimensional surface plots.

works with basic text files with, as far as I know,whitespace-delimited numbers.

Furthermore, gnuplot works with a number of different file formats for outputting

graphs, including GIF, JPEG, and PNG images, as well as more LaTeX-friendly formats

like postscript and encapsulated postscript.

I tried to lay this out to satisfy two different goals. First, I wanted it to be useful as a

step-by-step tutorial to ease would-be users into using gnuplot, and second, I wanted it

to serve as a useful reference (particularly to myself, most likely), which is why I would

expect the Table of Contents to be rather large.

Fold

Table of Contents

Why gnuplot?Setting up FontsRunning GNUPLOT and Getting HelpExecuting Basic Shell Commands in GNUPLOT

Gnuplot Command ShortcutsFunctionsList of operators and functions gnuplot knows about

Very Basic Plotting (and Replot) in gnuplotPlotting functionsPlotting dataMaking Plots PrettySelecting a TerminalTerminal propertiesTitles and Axis labels

Controlling How Axes LookSetting Axis RangesSetting Tic LevelsLegendsLabels

ArrowsPrint Variables in Legends and LabelsMore Advanced PlottingMaking functions look smoother
http://www.gnuplot.info/http://en.wikipedia.org/wiki/Whitespace_characterhttp://www.gnuplot.info/


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Changing How Lines and Points LookChanging line and point colors / stylesChanging Line Width and Point Size

Advanced Datafile PlottingPlotting data from different columnsTransforming Plotted Data

Adding Error BarsTwo X- and/or Y-axes in One Plot

Surface Plots (3-D plots)Plotting SurfacesMaking Surfaces Smoother and More Complete

Adjusting the Viewing AngleMaking a Contour PlotColorful SurfacesChanging Color SchemesDefining your own color rangeSurface Plots of Data FilesFitting Functions to Data

MultiplotMultiplot: Automatic layoutMultiplot: Creating your own layoutMargins

Why gnuplot?

You may ask, why pick gnuplot over some of the other plotting alternatives like Excel (o

some other spreadsheet), origin, matplotlib, etc.? I'll try to list some of the reasons I ca

think of, starting with the most important:

1. It is scriptable that is, you can spend a little bit of time getting your graph to loo

just the way you want it, then you have a script that will work for whatever data se

you have. Instantly. You only have to spend the time formatting a singlegraph, an

all other similar ones can be created instantly (and identically) from that template

2. It has an expansive built-in help function to help you every step of the way

3. It can print to an almost limitless number of file formats (terminals), so theterminal you want is almost certainly available

4. It is incredibly flexible, giving you control over almost every aspect of your graph

5. Once you become comfortable with gnuplot, it is fast and easy to create

customizable plots (especially once you've built up an army of scripts)

6. The learning curve isn't nearly as steep as you'd think with it being a command-


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line-only interface

7. It's widely used, so there are many, many tutorials and references around for

gnuplot (including this one).

8. It's free! Though not actually associated with the GNU project or the FSF (Free

Software Foundation). It's license is slightly more restrictive, not allowing you to

actually distribute your own modified versions of gnuplot though you can

distribute patches to modify certain versions.

Setting up Fonts

If you want to expand the fonts that gnuplotknows about when printing image files

(like GIF, PNG, JPG, etc.), you need to set the GDFONTPATHenvironment variable to

point to directories that contain font files.

For Mac OS X, this is typically

export GDFONTPATH=/Users//Library/Fonts

Using Cygwin on the PC, a typical choice is

export GDFONTPATH=/cygdrive/c/Windows/Fonts

On Linux, I typically keep a .fontsfolder in my home directory with all of my fonts in

it, so I would set

export GDFONTPATH=$HOME/.fonts

Running GNUPLOT and Getting Help

You can run gnuplot straight from a terminal (command-line) using the command

gnuplot. If it is available, you should see something like

bash$ gnuplot

G N U P L O T

Version 4.2 patchlevel 6


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last modified Sep 2009

System: Linux 2.6.32-36-generic

Copyright (C) 1986 - 1993, 1998, 2004, 2007 - 2009

Thomas Williams, Colin Kelley and many others

Type `help` to access the on-line reference manual.

The gnuplot FAQ is available from

http://www.gnuplot.info/faq/

Send bug reports and suggestions to

Terminal type set to 'wxt'

gnuplot>

(The terminal may be set to "aqua" on a Mac or "x11" on many other platforms.) This is

the main interface to Gnuplot. You can use the helpcommand to get interactive help

while inside the gnuplot interpreter. You can specify a command to get more pointed

help, too.

gnuplot> help plot

`plot` is the primary command for drawing plots with `gnuplot`.

It creates

plots of functions and data in many, many ways. `plot` is used

to draw 2-d

functions and data; `splot` draws 2-d projections of 3-d

surfaces and data.

`plot` and `splot` contain many common features; see `splot` fo

differences.

Note specifically that although the `binary `

variation does

work for both `plot` and `splot`, there are small differences


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between these

modes. Furthermore, `plot`'s `axes` option does not exist for

`splot`.

Syntax:

plot {}

{ | {"" {datafile-modifiers}}}

{axes } {} {with }

{, {definitions,} ...}

where either a or the name of a data file enclosed i

quotes is

supplied. A function is a mathematical expression or a pair ofmathematical

expressions in parametric mode. The expressions may be defined

completely or

in part earlier in the stream of `gnuplot` commands (see `user-

defined`).

It is also possible to define functions and parameters on the`plot` command

itself. This is done merely by isolating them from other items

with commas.

Press return for more:

etc.

Executing Basic Shell Commands in GNUPLOT

Sometimes you may find yourself wishing you could run a shell command while inside

gnuplot. Say, for instance, you forgot the name of the data file you wanted to plot, etc

You can execute some shell commands (like ls), using the !operator first. For instanc


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gnuplot> !ls

a.out nctest.f90 test.csv test_debug.f90 test.py

!

gnuplot>

You can also change directories using cd "directory_name"

Gnuplot Command Shortcuts

A very helpful thing to know before going too far is that gnuplot is very clever about

recognizing shortcuts as you become more advanced. Commands only need to be typed

out enough to make them uniquely identifiable by the interpreter. For instance, becaus

the quitcommand is the only command that starts with "q" in gnuplot, any of the

commands (q, qu, qui, or quit) will trigger that action.

Likewise, the lines

plot 'datafile' with lines

and

plot 'datafile' w l

are equivalent.

Functions

This section deals with generating mathematical functions, like

(1)

Functions are very useful because you can plot them, fit data to them, and modify data

using them. You can define a function via the following syntax:

gnuplot> f(x) = 3*x**2 + 2*x + 1

gnuplot>


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All 1-D functions should take xas its argument if you intend to plot them. If you plot a

parametric equation, both variables should be functions of t. For instance

gnuplot> f(t) = 1

gnuplot> g(t) = t

gnuplot>

plots a straight, vertical line if plotted as plot f(t), g(t), and a straight horizontal

line if plotted as plot g(t),f(t)

All 2-D equations take x,yas arguments if you plan to plot those. Additionally, you ma

define variables as coefficients. That is,

(2)

has three variable coefficients that are not arguments to the function. You can assign

values to these variables at any point (and change them whenever you want to), or you

can use them to fit to data. Assign a variable just like you assign an equation with an

equals sign.

gnuplot> a = 10

gnuplot>

List of operators and functions gnuplot knows about

I omit here the operators that are obvious, like +, -, /, and *.

**

exponential operator (a ** b is a raised to the power of b)

lognatural logarithm

log10

logarithm base 10

sin, cos, tan

normal trig functions sine, cosine, tangent


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sinh, cosh, tanh

hyperbolic trig functions

asin, acos, atan

arc-trig functions

asinh, acosh, atanh

arc-hyperbolic trig functions

gamma

gamma function

erfc

complementary error function

erf

error function

ceilceiling function (smallest integer greater than or equal to value)

floor

floor function (largest integer less than or equal to value)

Very Basic Plotting (and Replot) in gnuplot

This section deals with creating plots in gnuplot. You plot data by using the plot

command. The replotcommand will re-run the last plotcommand, but also takes th

same arguments that plottakes. Thus, you can either plot 2 items in the same plot

command via

gnuplot> plot 'datafile', f(x)

or you can do it in two steps via

gnuplot> plot 'datafile'

gnuplot> replot f(x)

Each plot command will completely erase any plot command(s) that came before it.

Plotting functions


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You can plot functions in one of two ways. To plot "normal" functions of a single

variable, the independent variable should always be x. For instance:

gnuplot> plot 3*x**2+2*x+1

gnuplot>

and

gnuplot> f(x) = 3*x**2+2*x+1

gnuplot> plot f(x)

gnuplot>

both plot equation (1) above, and should show a figure like this:

Plotting data

As an example, take the data from the attached file here(the first section is shown
http://jswails.wdfiles.com/local--files/using-gnuplot/plot_data_1.txt


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below)

0.0000000000000000 1.63187922851102197E-043

4.00801603206412792E-003 4.08358169487598205E-043

8.01603206412825585E-003 8.57322405816442756E-043

1.20240480961923846E-002 1.73129936161289217E-042

1.60320641282565117E-002 3.45784071201136770E-042

2.00400801603206405E-002 6.87578404252221707E-042

2.40480961923847693E-002 1.36344497652106874E-041

2.80561122244488981E-002 2.69730486896935522E-041

3.20641282565130234E-002 5.32407665559785807E-041

3.60721442885771557E-002 1.04855536367650238E-040

4.00801603206412810E-002 2.06050467205319491E-040

4.40881763527054132E-002 4.04009138612405269E-040

4.80961923847695386E-002 7.90394184633720358E-040

5.21042084168336639E-002 1.54287490021283476E-039

5.61122244488977961E-002 3.00504895188511843E-039

6.01202404809619215E-002 5.83990342350223851E-039

6.41282565130260468E-002 1.13238072759041723E-038

6.81362725450901791E-002 2.19084359508190369E-038

7.21442885771543113E-002 4.22923471384300249E-038

...

We can plot this data in one of 3 ways. We can plot just the points:

gnuplot> plot 'plot_data_1.txt' with points

gnuplot>


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with just lines connecting the points

gnuplot> plot 'plot_data_1.txt' with lines

gnuplot>


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or with points and lines connecting the points

gnuplot> plot 'plot_data_1.txt' with linespoints

gnuplot>


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Making Plots Pretty

Selecting a Terminal

One thing that can affect how your plot looks is which terminal (what image library you

choose to use to display your plot) you use and how you set that terminal up. You can g

a full list of available terminals by using the command set terminal

gnuplot> set terminal

Available terminal types:

aed512 AED 512 Terminal

aed767 AED 767 Terminal

aifm Adobe Illustrator 3.0 Format

bitgraph BBN Bitgraph Terminal

cgm Computer Graphics Metafile


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corel EPS format for CorelDRAW

dumb ascii art for anything that prints text

dxf dxf-file for AutoCad (default size 120x80)

eepic EEPIC -- extended LaTeX picture environment

emf Enhanced Metafile format

emtex LaTeX picture environment with emTeX specials

epslatex LaTeX picture environment using graphicx

package

epson_180dpi Epson LQ-style 180-dot per inch (24 pin)

printers

epson_60dpi Epson-style 60-dot per inch printers

epson_lx800 Epson LX-800, Star NL-10, NX-1000, PROPRINTER

... fig FIG graphics language for XFIG graphics edito

gif GIF images using libgd and TrueType fonts

gpic GPIC -- Produce graphs in groff using the gpi

preprocessor

hp2623A HP2623A and maybe others

hp2648 HP2648 and HP2647

hp500c HP DeskJet 500c, [75 100 150 300] [rle tiff]Press return for more:

On MacOS X, aquais a good terminal to use (and is default if you install gnuplot

from MacPorts). You can also save aquaplots as PDF files directly in the aqua

application window.

On Ubuntu,wxtis a nice-looking terminal with several options.

On other systems where these may not be available, x11is a good default terminaTo save images, you can use any of the image file formats (gif, jpeg, png), or you

can use a postscript or encapsulated postscript (some gnuplot installations have

variants specific for LaTeX).

Terminal properties


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The main way you can adjust the look of your plot is not which terminal you choose, bu

the options that you choose to customize it. You can specify the default text, text size,

and graph size. For instance, look at how the selection of terminal below affects the

appearance of the plotted data with points (second image on this page):

gnuplot> set terminal gif font 'calibri,20' size 800,600 enhance

Terminal type set to 'gif'

Options are 'nocrop enhanced font calibri 20 size 800,600 '

gnuplot> set output 'plot_1_gifterm.gif'


gnuplot> quit

I will describe the bits of the command set terminal gif font 'calibri,20'


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size 800,600 enhanced:

set terminal gif: This command sets the terminal to the gifimage format

font 'calibri,20': This sets the default font to be of type "calibri" with a fon

size of 20 pt.

size 800,600: This sets the size of the image to be 800 pixels by 600 pixels

enhanced: This keyword allows some more advanced formatting. For instance,

the string "x^2"will be expanded wherever it is displayed in the terminal as x2

and "pK_a"will be displayed as pKa. We will see this effect when we do some

examples below with applying labels.

Titles and Axis labels

Good plots should have titles and labels for all of the axes. You can specify the font typeand size to override the terminal defaults for each of these if you want. In this way, you

can create plots that have a large title, smaller axis labels, and an even smaller legend/t

mark labels.

The title is set via set title

The x-axis label is set via set xlabel

The y-axis label is set via set ylabel

Look at the effect that the below code has on our last GIF image.




gnuplot> set output 'plot_1_titled_gifterm.gif'

gnuplot> set title 'A Data File Plotted With Points' font

'calibri,25'

gnuplot> set xlabel 'Domain_{independent variable}' font

'calibri,18'

gnuplot> set ylabel 'Range' font 'calibri,18'


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gnuplot> quit

Controlling How Axes Look

Another key to making great-looking plots is to adjust the window to zoom in on the ar

of interest. You may also want to control how the axes are printed (for instance, do you

want the plot area enclosed in a box with axes on either side, or just an x-axis on thebottom and y-axis on the left?). You can also control where (or even if) the major and

minor tic marks are placed, and how frequently they appear.

Setting Axis Ranges

To set the range for the X-axis, use the keyword xrange. For example


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set xrange [:]

To set the range for the Y-axis, use the keyword yrangein exactly the same way (and

the same for zrangeif you're doing a surface plot).

The defaults for data files are generally pretty decent, since it simply zooms in around

the maxima and minima of the various data sets, but for functions it is generally prettyhorrendous (as well it should be how are the gnuplot programmers to know what par

of the curve you think is interesting?).

Setting Tic Levels

To set the tics on the various axes, use the set xticscommand (or yticsor ztics

depending on what axis you wish to control). The full command is:

set xtics [mirror | nomirror] [in | out] [autofreq | |

, | ,,] [norotate | rotate]

The meaning of each is as follows:

mirror | nomirror: mirror(default) means draw tics on the opposite side o

the plot as well. nomirrormeans only draw tics on the side by the labels.

in | out: Either the tics are drawn into the plot (away from the edge of the

image) or outof the plot (toward the edge of the image)

autofreq | | ,[,]: The frequency of the ti

is chosen either automatically (autofreq, or the start and stop are chosen

automatically but the interval is controlled ({}), or the start and interval

between tics are controlled (,), or the start, stop, and intervals

are all controlled (,,).

norotate | rotate: Either rotate (or not, by default) text to align with the

direction of the tic marks. For instance, it will rotate the labels on the X-axis by

90o, but keep the labels on the Y-axis horizontal.

For example, take a look at the code below to see how I zoomed in on the region of

interest in the data plot and how I modified the look of the X-axis in particular. Notice


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that the tic marks are going out of the plot area, unlike the Y-axis, and that there are no

tic marks on the opposite side, unlike the Y-axis. Also notice how the text is rotated for

the tic labels.




gnuplot> set output 'plot_1_titled_zoomed.gif'


'calibri,25'


'calibri,18'


gnuplot> set xrange [0.8:1.75]

gnuplot> set xtics nomirror out 1.0,0.125,1.75 rotate


gnuplot> quit


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Legends

Another common feature of plots that impacts how it looks is the legend, or the key. In

every example above, the key has just been the default key. The default key is the

function that was plotted (if f(x)is plotted, then the text is f(x).

To remove the legend completely, use the command

unset key

If you want the legend, you can do a number of things with it. You can reposition it

around the plotted area, you can enclose it in a box, or you can give the legend a title.

You can also control the label that each plotted function or data file is given in the key o

the plot command. See how the last figure is affected by modifying the key:


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gnuplot> set output 'plot_1_titled_key_gifterm.gif'


'calibri,25'


'calibri,18'

gnuplot> set ylabel 'Range^{dependent variable}' font

'calibri,18'

gnuplot> set key left top title 'Plot Legend' box linewidth 2

gnuplot> plot 'plot_data_1.txt' with points title 'Data From

File'gnuplot> quit


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The command that controls the key is decomposed as follows:

set key: Turns the key on (unset keyturns the key off)

left: Aligns the key to the left of the plot area (inside by default, the keyword

outsidewill put it outside the plot area)

top: Aligns the key to the top. At this point, it will be at the top-left hand corner o

the plot area

title 'Plot Legend': Gives the legend a title

box: Encloses the legend in a box

linewidth 2: Doubles the default line width of the box

Note that you can prevent gnuplot from printing a particular plotted object (function o

data file) by setting the title to an empty string:


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plot 'data_file.txt' with lines title ''

Labels

You can also add any number of labels that you want to the graph. Notice the label

added by the code below:




gnuplot> set output 'plot_1_titled_key_labeled_gifterm.gif'


'calibri,25'


'calibri,18'



gnuplot> set label 1 "Printed label" font 'calibri,14' at

0.25,-1.5 left textcolor rgbcolor "#0000FF"


File'gnuplot> quit


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The command that controls the label is decomposed as follows:

set label 1: Creates a label whose ID is 1, so any reference to label 1 will resolv

to this label. It can be any integer

"Printed label": The text of the label

font 'calibri,14': Sets the font and font size of the label

at 0.25,-1.5: Puts the label at these coordinates (not pixels, but the

coordinates in the coordinate system of the plot)

left: The point described via the atkeyword is placed at the leftof this text bloc

textcolor rgbcolor "#0000FF": Sets the color of the label to the

hexadecimal value 0000FF (0 Red, 0 Green, 255 Blue). The default color is just

black.


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Arrows

Sometimes you want to draw attention to something on a graph using an arrow. So you

want to combine an arrow with a label to point something out. To print an arrow to the

plot, use set arrow. The syntax is as follows:

set arrow from to [nohead | head| backhea| heads] [arrowstyle ]

To print a line, use nohead. The default, which prints an arrow head at the toposition

has the keyword head. To put an arrow head at the fromposition, use the backhead

keyword, and to have a double-headed arrow, use the keyword heads. You can control

the arrow style via the arrowstyle , much like you can control the

line style or point style. Also like the line and point styles, these are terminal-dependen

so play around and see what you like best.

An example using this syntax is shown below, adding onto the previous example. Notic

how I use the position of the label and the leftkeyword to control the relative

placement of the arrow and the label very easily. You should use the location keyword

for the label that matches the position you want the arrow to take with respect to the

label. In the next example, I want the arrow placed on the right side of the label.

gnuplot> set output 'plot_1_titled_key_labeled_arrow.gif'


'calibri,25'


'calibri,18'



gnuplot> set label 1 "Turning Point" font 'calibri,14' at

0.5,-1.5 right textcolor rgbcolor "#0000FF"

gnuplot> set arrow 1 from 0.5,-1.5 to 0.85,0.01 linetype -1

linewidth 2



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File'

gnuplot> quit

Print Variables in Legends and Labels

There may come a point where you define a variable that has some value (whether it's

given that value during fitting a function to some data or whether you assign it yourself

and you wish to include that variable's value in a legend entry or a label. To do that, youdefine the string the same way you would in a C program using sprintf(). Instead

of defining a string like:

title 'a = 10'

you can use


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More Advanced Plotting

When I first introduced plotting above, I described how to customize your plots a little

bit by plotting with points, lines, or both lines and points (these are valid for both

functions and data, alike). Now I will get into some more advanced ways of adjusting th

appearance of your plots.

Making functions look smoother

The way gnuplot plots functions is to evaluate your function at a number of equal-space

intervals and connect those points with lines. Thus, in order to get a smooth curve, thes

points must be significantly closer together than the span in which the function turns

around. The default number of points that gnuplot uses is 100. For the functions plotte

above, the plots are clearly smooth because the function does not radically change


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direction within 1/100 of the space of the graph. Let's consider the function sin(4*x)

though, and see what happens when we plot that function.




gnuplot> set output "sin4x_normal_sample.gif"

gnuplot> unset key

gnuplot> plot sin(4*x)

gnuplot> quit

Notice how jagged the points of the function are, since there are areas of the curve in

which the curvature is very large compared to the spacing between the sampling points


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To smooth this function out, we need to take more samples. We can do this via the

command

set samples

where the given is the number of samples you wish to take. Note that the

higher this number is the smoother your plot will be, but the longer the plot will take torender. (This isn't as much a problem for 1-D plots as it is for 2-D surface plots where

there are samples in both axes and the number of points scales as the product of the tw

sampling numbers). See how we modify the above plot by using set samples:

gnuplot> set term gif font 'calibri,12' size 800,600 enhanced



gnuplot> set output "sin4x_1000samples.gif"

gnuplot> unset key

gnuplot> set samples 1000

gnuplot> plot sin(4*x)

gnuplot> quit


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Notice how the curve is much smoother and how it actually reaches its correct max and

min values (1 and -1, respectively).

Changing How Lines and Points Look

Gnuplot also gives us control over how our lines and points look. We can give our lines

and points different colors, different styles, and different sizes or thickness. This applie

to both Function plotting and Data File plotting

Changing line and point colors / styles

To change the color or style of the line or point, use the linetype(or lt) keyword

followed by an integer. Different terminals typically have different colors and/or styles

for different values, so you'll need to experiment a little bit to figure out which integer


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line type corresponds with which style. In my experience, the type index -1 corresponds

to black in colorful terminals.

Changing Line Width and Point Size

Lastly, you can vary how thick the lines appear or how big the points appear by using

linewidth or pointsize . The factoris a multiplicativescaling factor that determines the size or thickness by multiplying the "default" thickne

or size by that factor. Thus, by definition, factors of 1 are default.

An example combining all of these concepts on our data file:




gnuplot> set output 'plot_1_new_styles.gif'

gnuplot> unset key

gnuplot> plot 'plot_data_1.txt' with linespoints linetype -1

linewidth 3 pointsize 1.5

gnuplot> quit


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Advanced Datafile Plotting

Sometimes a simple plot 'datafile' with linessimply doesn't do what you

want it to do. For instance, sometimes you want to adjust the value of the x-axis by a

factor to transform "frame number" into "time", or you don't want to use the first two

columns of data in the file.

Still other times you may want to adjust a data set according to some function (forinstance if you have fit a function and wish to subtract the value of that fitted function t

look at residual errors or something). That is what this section addresses.

Also, you may want to add error bars to your data points, or you may want to plot

histograms or bars instead of the traditional points and lines.


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Likewise, you can transform data by a function as well either a user-defined function

or a built-in function like log10(). For example, below I translate the whole plot 2 units

up and turn the X-axis into a logarithmic scale.

gnuplot> set term gif font 'calibri,12' size 800,600 enhanced



gnuplot> set output 'plot_1_modified_translated_xaxis.gif'

gnuplot> unset key

gnuplot> plot 'plot_data_1.txt' using (log10($1)):($2+2) with

points

gnuplot> quit


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Adding Error Bars

gnuplot makes it very easy to add error bars. The values for the error bars must be adde

as an additional data column in your data file (and can be selected via the usekeyword

as described above for selecting X- and Y- values). The error bar columns can take a

number of formats that will be understood by gnuplot:

: A single column describing how wide the error bars should be with thedata point placed in the center. Only X- or Y- error bars can be chosen with this

: 2 Data columns describing the low end of the error bar and the

high end of the error bar. This is how 2 columns are interpreted when only X- or Y

error bars are asked for.

: 2 Data columns describing the width of the X-error ba


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and the Y-error bars with the data point in the middle. This is how 2 columns are

interpreted when both X- and Y- error bars are asked for.

: 4 Data columns describing both

ends of the error bars in both the X- and Y- directions. If 4 columns are specified,

both X- and Y-error bars must be turned on.

Note that we don't reallyneed all of the columns that are available if we are able to

specify something else for the error bars with the usingkeyword. The code below will

add error bars of full width 0.2 (so 0.1 on either side of the point) in the Y-direction

using the same data file we've been using so far:



Options are 'nocrop enhanced font calibri 12 size 800,600 'gnuplot> set output 'plot_1_with_errorbars.gif'

gnuplot> unset key

gnuplot> plot 'plot_data_1.txt' using 1:2:(0.2) every 10 with

yerrorbars, 'plot_data_1.txt' with lines linetype -1

gnuplot> quit


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bounded between -1 and 1, whereas your data may be anywhere. Therefore, you will set

the left Y-axis to the data and the right Y-axis to the autocorrelation function.

There is a second X- and Y- axis that you can modify (x2and y2). You can modify them

just like any other. (e.g., set y2range [-1:1]). Then you can specify axes

[x1y1|x1y2|x2y1|x2y2]on the plotline for any graph to select the two axes you

want that function or data to be plotted against.

An example script is shown below with the resulting graph (data is available here):

set term gif font 'calibri,16' size 1024,768 enhanced

set output 'deprot_traj_prot_rlx.gif'

set y2range [-1:1]

set ytics nomirror

set y2tics out -1,0.2,1 nomirror

set title 'Deprot. Traj Relaxation Energy and Autocorrelation'

font 'calibri,25'

set ylabel 'Energy (kcal/mol)' font 'calibri,20'

set y2label 'Autocorrelation Value' font 'calibri,20'

set xlabel 'Time or Lag (ps)' font 'calibri,20'

plot 'deprot_traj_prot_rlx_deprot_minus_prot.dat' \

u ($1*0.02):2 w l lw 2 axes x1y1 title 'Energy Difference',

\

'deprot_traj_prot_rlx_deprot_minus_prot_corr.dat' \

u ($1*0.02):2 w l lw 2 axes x2y2 title 'Autocorrelation'

The resulting plot is here:
http://jswails.wdfiles.com/local--files/using-gnuplot/deprot_traj_prot_rlx_deprot_minus_prot.dat


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Surface Plots (3-D plots)

Here I will discuss how to generate and modify surface plots for both functions of 2

variables and data with 2 variables. I will demonstrate surface plots and their features

using functions and introduce plotting 2-D data at the end.

Plotting Surfaces

Surface plots have a different command: splot. However, it is analogous to plotin

many ways. While a plotted function should be some function of x, functions for a

surface plot should be functions of xand y. For example:




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gnuplot> set output 'splot_function.gif'

gnuplot> unset key

gnuplot> f(x,y)=sin(x)*cos(y)

gnuplot> splot f(x,y)

gnuplot> quit

Surfaces are plotted as a series of cross-sections drawn onto a 3-D grid. Each cross-

section is plotted like a regular 2-D function. That is, at the given value of x or y, the 3-D

function is sampled a given number of times (100 by default see set samplesin th

function smoothing above). The frequency with which these cross-sections are sampled

is controlled by the isosamplesvariable.


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Making Surfaces Smoother and More Complete

You can see that this surface is not particularly clear, since the sampling of the cross-

sections is fairly infrequent. You can increase the number plotted cross-sections by usin

the set isosamplescommand, and you can improve the resolution of each cross-

section by using the set samplescommand as we've already demonstrated for 2-D

functions. Be careful with this, though. The number of points that need to be calculated

(and thus the time it takes to render a surface) grows veryquickly as you increase the

number of isosamples. See how the above graph is modified when we increase the

number of isosamples from its default value of 10 to 100:



Options are 'nocrop enhanced font calibri 12 size 800,600 'gnuplot> set output 'splot_function_many_isosamples.gif'

gnuplot> unset key


gnuplot> set isosamples 100


gnuplot> quit


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Adjusting the Viewing Angle

Adjusting the viewing angle is controlled by set view. It is used as follows:

set view [,]

It defines a rotation around the X-axis (x_rot) and optionally a rotation around the Z-

axis (rot_z). The initiallayout (before any rotations are applied, or under set view

0,0, is a right-handed coordinate system with the positive X-axis as the horizontal axis

pointing to the right, the positive Y-axis as the vertical axis pointing up, and the positiv

Z-axis as the axis coming out of the screen directly at you. The default view is equivalen

to

set view 60,30


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Play around with this to get comfortable with it.

Making a Contour Plot

Many times what you are interested in is a contour plot. To make a contour plot of the

function we plotted above, use

set contour [base | surface | both]

The most common option is base, which puts the contours on the X-Y plane. surface

puts the contour lines on the surface, and bothputs the contour lines on both the

surface and the X-Y plane.

And to control the look of the contour lines, we use

set cntrparam

There are 2 different (common) cntrparams that are often modified.

set cntrparam [linear | cubicspline | bspline]

The above controls the interpolation method between points on the same isoline.

lineardraws straight lines between adjacent points, whereas

cubicsplineinterpolates the values between them using (you guessed it) cubic splines. This results i

a much smoother plot. bsplineresults in an even smoother plot, but actually

approximates the values knownto be on a given isoline.

If you choose bspline, you can choose the order of the spline used to interpolate via

set cntrparam order

where n is an integer

See how we add contour lines to the plot above:




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gnuplot> set output 'splot_function_contour_with_surface.gif'


gnuplot> set key outside top right


gnuplot> set contour base

gnuplot> set cntrparam levels auto 10


gnuplot> quit

If wejustwant to see the contour plot, we can remove the surface and adjust the view t

look head-on:


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gnuplot> set output 'splot_function_contour_without_surface.gif




gnuplot> set contour base

gnuplot> set cntrparam levels auto 10

gnuplot> unset surface

gnuplot> unset ztics

gnuplot> set view 0,0

gnuplot> splot f(x,y)gnuplot> quit


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Colorful Surfaces

Since version 4.0 (or something around there), gnuplot added the ability to add colored

surfaces via set pm3d. The command is formatted as:

set pm3d [at b | at t | at s]

where you can put the colored map superimposed on the surface, as a flat image at the

bottom, or as a flat image at the top. In all of these cases, it is probably a good idea to

turn the surface off for the same reason as we turned off the surface in the above contou

plot example.

An example is shown below:



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gnuplot> set output 'splot_function_pm3d.gif'




gnuplot> set pm3d at s



smooth palette in gif: using 160 of 160 available color position

gnuplot> quit

Changing Color Schemes


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Gnuplot offers almost infinite flexibility when it comes to setting the color scheme for

your plots so that you're not limited to the scheme above. You can choose color scheme

in grayscale as well, for plots that will be entering a black-and-white publication or

something.

On this pageis a reference for different color schemes that some may think are pretty

and the RGB formulae used to produce them.

There are many ways of specifying colors (in different color spaces, even). For the

purposes of this tutorial/reference, though, we will stick with RGB (Red/Green/Blue)

color space, and setting palettes via the rgbformula. This formula is a built-in formul

that gnuplot uses to interpolate colors at different values of the color range, and is

defined by 3 colors.

The gnuplot help function provides 7 nice-looking RGB formula presets (including the

default one). They are, starting with the default:

7,5,15 traditional pm3d (black-blue-red-yellow)

3,11,6 green-red-violet

23,28,3 ocean (green-blue-white); try also all other

permutations

21,22,23 hot (black-red-yellow-white)

30,31,32 color printable on gray (black-blue-violet-yellow

white)

33,13,10 rainbow (blue-green-yellow-red)

34,35,36 AFM hot (black-red-yellow-white)

To change the color scheme, use the following command:

set palette rgbformulae ,,

As an example, the script above changes the palette to 33,13,10 for a rainbow image:


http://jswails.wikidot.com/gnuplot-color-schemes


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gnuplot> set output 'splot_function_pm3d_rainbow.gif'





gnuplot> set palette rgbformulae 33,13,10




gnuplot> quit

Defining your own color range


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Perhaps you want to play around and develop your own color scheme. The easiest way

do this is by defining a color ladder. What I mean by this is you define the colors that

your plot has at various values, and gnuplot will interpolate between these for you. For

instance let's create a color scheme that moves from royalbluethrough turqouise

through yellowand finally ending on red. (To get a full list of colors that gnuplot has

assigned names to, use the command show colornames).

To set this palette with our proposed color scheme for our plot, use the command

set palette defined (0 "royalblue",1 "turquoise",3 "yellow",5

"red")

This is normalized to span 0 to 1, so in this way it is easier to control how quickly each

color shift happens in the palette. The effect of using this palette is:




gnuplot> set output 'splot_function_pm3d_custom_palette.gif'





gnuplot> set palette defined (0 "royalblue",1 "turquoise",3

"yellow",5 "red")




gnuplot> quit


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If you have found a color scheme that you like, you should fit this pre-defined color

scheme to gnuplot's rgbformulae. They make this very easy via show palette

fit2rgbformulae. Gnuplot will fit our color palette to -10,-13,-26.

gnuplot> set palette defined (0 "royalblue",1 "turquoise",3

"yellow",5 "red")

gnuplot> show palette fit2rgbformulae

The best match of the current palette corresponds to

set palette rgbformulae -10,-13,-26

gnuplot>

Let's see how our plot changes when we set the palette via these rgbformulae compared


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to the last image:




gnuplot> set output

'splot_function_pm3d_custom_palette_rgbform.gif'





gnuplot> set palette rgbformulae -10,-13,-26




gnuplot> quit


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The two images are very similar.

Surface Plots of Data Files

So far we've seen surface plots of functions. There's no additional differences between

data files and functions for splotthat don't already exist for plot, so I focus here just

on the format requirements for surface plot data.

Every line that comes directly after the previous line will be connected to the point

before it if plotted with lines. The way data files are typically formatted for surface

plotting is to plot isolines in the same way gnuplot plots function surfaces. If you do no

have a blank line between different isolines, though, gnuplot will connect them, making

your surface look very strange.


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In order to get a "good"-looking surface plot, you should make sure that a space (and

only a single space!) exists between isolines.

This first filedoes not have the spaces between isolines. This second filedoes. See how

the two differ:

The above image was created with this script.

Notice how the surface plot on the left is nicely gridded (it's a fine grid, so may be

difficult to see), but the surface plot on the right is not, and appears to have sharp Vs

running up and down the Y-axis. That's because gnuplot was never told (by a blank line

to disconnect points from different isolines.

Fitting Functions to Data

Another very powerful aspect of gnuplot is its ability to fit arbitrary functions to

arbitrary data using arbitrary adjustable (fitting) parameters. To fit a function to data,

use the fitcommand as follows:

fit 'datafile' using : via

,,,

That data file I will be using in this section for examples can be found here, which is a

relaxed energy surface of a dihedral scan calculated with a quantum mechanical metho

This data should be periodic, since dihedral angles themselves are periodic, so I will

choose a truncated form of a Fourier series expansion to fit this data to. Furthermore, I
http://jswails.wdfiles.com/local--files/using-gnuplot/quantum_profile.txthttp://jswails.wdfiles.com/local--files/using-gnuplot/compare_spaces.gnuhttp://jswails.wdfiles.com/local--files/using-gnuplot/splot_spaces_comparison.gifhttp://jswails.wdfiles.com/local--files/using-gnuplot/surface_data_with_spaces.txthttp://jswails.wdfiles.com/local--files/using-gnuplot/surface_data_without_spaces.txt


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will only pick even terms, since that is the form of the data. The formula I'm going to us

is

(3)

The code below, when run as a script, produces the accompanying image. Notice the

elements of this script it combines most of what we used above to generate this plot.After you run the script, you will see a file called fit.logthat has the verbose output

the fitting procedure, including statistics that can help you measure the quality of the fi

Note that for many kinds of fitting, there is no analytical solution to the best fit, and so

an iterative procedure must be used until self-consistency is achieved. In this case, a ba

initial choice for some parameters may prevent a good fit from ever being achieved (thi

is because of the mathematics involved, not because of a shortcoming of gnuplot). To g

around this, you'll need to provide a better initial guess (I believe the default is zero, bu

don't quote me on that). To do that, just assign the variable to a value before you run th

"fit" command.

set terminal gif font 'calibri,14' size 800,600 enhanced

set output "quantum_scan_fit.gif"

f(x) = a + b*cos(2*x) + c*cos(4*x) + d*cos(6*x) + e*cos(8*x) +

f*cos(10*x) + g*cos(12*x)

set title "Quantum Dihedral Scan" font 'calibri,25'

set xlabel "Dihedral Angle (Radians)" font 'calibri,18'

set ylabel "Potential Energy (kcal/mol)" font 'calibri,18'

set key top left

set samples 1000

fit f(x) 'quantum_profile.txt' using 1:2 via a,b,c,d,e,f,g
http://jswails.wdfiles.com/local--files/using-gnuplot/quantum_scan_fit.gnu


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plot 'quantum_profile.txt' with points pointsize 2.5 pointtype 3

title '', \

f(x) with lines linetype -1 linewidth 2 title

sprintf("a=%.3f, b=%.3f,\nc=%.3f, d=%.3f,\ne=%.3f,

f=%.3f,\ng=%.3f",a,b,c,d,e,f,g)

Multiplot

The multiplotoption allows you to plot multiple graphs in the same canvas. For

instance, embedded graphs, a grid of graphs, etc. The way this is done is via

gnuplot> [set up your graph here]

gnuplot> set multiplot [layout rows,cols]

gnuplot> [set up your first graph]


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gnuplot> [plot your first graph]

gnuplot> [set up your second graph]

gnuplot> [plot your second graph]

gnuplot> ... etc

gnuplot> unset multiplot # Now you are done

gnuplot> quit

Multiplot: Automatic layout

The layoutkeyword will set up the graphs in a grid where rowsis the number of rows

and colsis the number of columns. It will then fill in the graphs from left to right alon

rows. The code block below plots six different polynomials in different plots in the sam

image. See how the graphs are filled in according to the 3x2 layout.

gnuplot> set terminal gif size 1200,600 enhanced


Options are 'nocrop enhanced font arial 12 size 1200,600 '

gnuplot> set output 'multiplot_functions.gif'

gnuplot> unset key

gnuplot> set multiplot layout 2,3

multiplot> set title "x^2"multiplot> plot x**2

multiplot> set title "x^3-x"

multiplot> plot x**3-x

multiplot> set title "sin(x)"

multiplot> plot sin(x)

multiplot> set title "x**4-x**2+1"

multiplot> set yrange [0:10]multiplot> set xrange [-5:5]

multiplot> plot x**4-x**2+1

multiplot> set title "x^5"

multiplot> set yrange restore

multiplot> set xrange restore


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multiplot> plot x**5

multiplot> set title "x"

multiplot> plot x

multiplot> unset multiplot

gnuplot> quit

Multiplot: Creating your own layout

Sometimes you don't want to snap a separate plot to a grid. For instance, suppose you

want 3 graphs, the first graph occupies the top half of the image, the second occupies th

bottom left quarter, and the third occupies the bottom right quarter. Also, you may wan

a graph embedded in another graph. These require specific control of your layout, and

requires you to specify the location and size of each of your graphs.

To set the location of your first plot, use set originlike so:

set origin ,

Here, is a number between 0 and 1 that specifies the where along thehorizontal axis the origin of your plot will be (this is the edge of your margins, not the

edge of your actual plot). For instance, to have your plot start at the left edge of the

screen, use as your . To have it start in the middle of the screen, use 0.

as your .

To control how large that particular plot is, use set sizelike so:
http://jswails.wdfiles.com/local--files/using-gnuplot/multiplot_functions.gif


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set size ,

Again, and are numbers between 0 and 1 that determine what

fraction of the screen it will take up.

So, to create the layout we described above (with 3 plots), you would use the following

template:

gnuplot> set multiplot

multiplot> set origin 0,0.5

multiplot> set size 1,0.5

multiplot>

multiplot> set origin 0,0

multiplot> set size 0.5,0.5

multiplot>

multiplot> set origin 0.5,0


multiplot> multiplot> unset multiplot # now you're done

gnuplot> quit

An example, with the result, is shown below:

gnuplot> set term gif


Options are 'nocrop font arial 12 size 640,480 '

gnuplot> set output 'custom_multiplot.gif'

gnuplot> set multiplot

multiplot> set origin 0,0.5

multiplot> set size 1,0.5

multiplot> plot sin(x)


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multiplot> set origin 0,0


multiplot> plot x**3

multiplot> set origin 0.5,0


multiplot> set xrange [-5:5]

multiplot> set yrange [0:10]

multiplot> plot x**4-x**2+1

multiplot> unset multiplot

gnuplot> quit

Margins

If you want to get rid of the spaces in between adjacent plots, you'll need to set margins

between your multiplots. You can do this via the following variables:

set tmargin # Sets the margins on the tops of the plot

set bmargin # Sets the margins on the bottoms of the

plots
http://jswails.wdfiles.com/local--files/using-gnuplot/custom_multiplot.gif


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set lmargin # Sets the margins on the left of the plots

set rmargin # Sets the margins on the right side of the

plots

After you do these, don't forget to properly remove any tics from axes you don't want

labeled (e.g. any plots on "top" that you just want to correspond to the tics on the plots

below) as well as axis labels. Play around and see what you get.

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